The centre in the Wellington Park area of the city was targeted at about 10pm on Thursday night.
A milk bottle filled with paint was thrown at the building and two teenage boys were seen running away from the area.
A number of mosques have been attacked in England in the wake of the murder on Wednesday of soldier Lee Rigby by terrorists in London.
No one was injured in the criminal damage incident in Belfast.
Anyone who witnessed it or who has any information is asked to contact police.
COMMENT RULES: Comments that are judged to be defamatory, abusive or in bad taste are not acceptable and contributors who consistently fall below certain criteria will be permanently blacklisted. The moderator will not enter into debate with individual contributors and the moderator’s decision is final. It is Belfast Telegraph policy to close comments on court cases, tribunals and active legal investigations. We may also close comments on articles which are being targeted for abuse. Problems with commenting? email@example.com